# Alfvén waves

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## Alfvén waves

Propagating oscillations in electrically conducting fluids or gases in which a magnetic field is present. Magnetohydrodynamics deals with the effects of magnetic fields on fluids and gases which are efficient conductors of electricity. Molten metals are generally good conductors of electricity, and they exhibit magnetohydrodynamic phenomena. Gases can be efficient conductors of electricity if they become ionized. Ionization can occur at high temperatures or through the ionizing effects of high-energy (usually ultraviolet) photons. A gas which consists of free electrons and ions is called a plasma. Most gases in space are plasmas, and magnetohydrodynamic phenomena are expected to play a fundamental role in the behavior of matter in the cosmos. See Plasma (physics)

Waves are a particularly important aspect of magnetohydrodynamics. They transport energy and momentum from place to place and may, therefore, play essential roles in the heating and acceleration of cosmical and laboratory plasmas. A wave is a propagating oscillation. If waves are present, a given parcel of the fluid undergoes oscillations about an equilibrium position. The parcel oscillates because there are restoring forces which tend to return it to its equilibrium position. In an ordinary gas, the only restoring force comes from the thermal pressure of the gas. This leads to one wave mode: the sound wave. If a magnetic field is present, there are two additional restoring forces: the tension associated with magnetic field lines, and the pressure associated with the energy density of the magnetic field. These two restoring forces lead to two additional wave modes. Thus there are three magnetohydrodynamic wave modes. However, each restoring force does not necessarily have a unique wave mode associated with it. Put another way, each wave mode can involve more than one restoring force. Thus the usual sound wave, which involves only the thermal pressure, does not appear as a mode in magnetohydrodynamics. The three modes have different propagation speeds, and are named fast mode (F), slow mode (S), and intermediate mode (I). The intermediate mode is sometimes called the Alfvén wave, but some scientists refer to all three magnetohydrodynamic modes as Alfvén waves. The intermediate mode is also called the shear wave. Some scientists give the name magnetosonic mode to the fast mode.

#### Basic equations

The magnetohydrodynamic wave modes are analyzed by using the magnetohydrodynamic equations for the motion of a conducting fluid in a magnetic field, combined with Maxwell's equations and Ohm's law. See Maxwell's equations

It is possible to combine Ohm's law with Faraday's law of induction. The resultant equation is called the magnetohydrodynamic induction equation, which is the mathematical statement of the “frozen-in” theorem. This theorem states that magnetic field lines can be thought of as being frozen into the fluid, with the proviso that the fluid is always allowed to slip freely along the field lines. It is the coupling between the fluid and the magnetic field which makes magnetohydrodynamic waves possible. The oscillating magnetic field lines cause oscillations of the fluid parcels, while the fluid provides a mass loading on the magnetic field lines. This mass loading has the effect of slowing down the waves, so that they propagate at speeds much less than the speed of light (which is the propagation speed of waves in a vacuum). See Electromagnetic radiation, Light

#### Linearization of equations

Unfortunately, the basic equations are too difficult to be of much use because some of them are nonlinear; that is, they contain products of the quantities for which a solution is sought. Nonlinear magnetohydrodynamics is still only in its infancy, and only a few specialized solutions are known. In order to get solvable equations, scientists accept the limitation of dealing with small-amplitude waves and linearize the equations, so that products of the unknowns are removed. Fortunately, much can still be learned from this procedure; the resulting equations have solutions which are harmonic in time and space. See Harmonic motion

#### Intermediate mode

The motions in this mode are pure shears. There is no compression of the plasma. The tension in the magnetic field lines is the only restoring force involved in the propagation of the wave. This mode is therefore closely analogous to the propagation of waves on a string.

Because these waves channel energy along magnetic fields, they may be responsible for the observed fact that cosmical plasmas are strongly heated in the presence of magnetic fields.

#### Fast mode

This mode is difficult to analyze. However, many cosmical and laboratory plasmas satisfy the strong-magnetic-field case where the fast mode is more easily understood.

Fast waves are compressive, and the magnetic field strength fluctuates as well. Thus fast waves are governed by the two restoring forces associated with the tension and pressure in the magnetic field.

The fast mode can propagate energy across the magnetic field.

#### Slow mode

Like the fast mode, the slow mode is difficult to study in general, and the discussion will again be confined to strong magnetic fields. The slow mode in a strong field is equivalent to sound waves which are guided along the strong magnetic field lines. The strong magnetic field lines can be thought of as a set of rigid pipes which allow free fluid motion along the pipes, but which restrict motion in the other two directions. The motions on the individual pipes are not coupled together, and thus the slow mode is analogous to the sound waves on a set of independent organ pipes. The slow mode channels energy along the magnetic field. Because the sound speed is small, by assumption, the slow mode transmits energy less effectively than the fast or intermediate modes.

#### Nonlinear effects

Only small-amplitude waves have been considered. Real waves have finite amplitude, and nonlinear effects can sometimes be important. One such effect is the tendency of waves to steepen, ultimately forming magnetohydrodynamic shock waves and magnetohydrodynamic discontinuities. There is an abundance of magnetohydrodynamic discontinuities in the solar wind. See Shock wave

It is also possible that waves can degenerate into turbulence. There are indications that this too happens in the solar wind. See Turbulent flow

#### Surface waves

Only waves in a spatially uniform background have been considered. While the analysis of magnetohydrodynamic waves in a nonuniform background is complicated, it is possible to consider an extreme limit, in which the background is uniform except at certain surfaces where it changes discontinuously. Surfaces can support magnetohydrodynamic waves, which are in some respects similar to waves on the surface of a lake. These waves may play important roles in heating cosmical and laboratory plasmas. See Magnetohydrodynamics

McGraw-Hill Concise Encyclopedia of Physics. © 2002 by The McGraw-Hill Companies, Inc.

## Alfvén waves

(al-ven ) Disturbances transmitted through a plasma in the presence of a magnetic field. The direction of propagation is parallel to the mean magnetic field, with the plasma particles vibrating at right angles to this direction. The speed of propagation, the Alfvén speed, depends on the magnetic field strength and the plasma density. The waves interact with the plasma particles, for example by exerting radiation pressure on the plasma. As the waves dissipate, the plasma particles are heated and accelerated. Alfvén waves are a type of magnetohydrodynamic (MHD) wave. They have been directly observed in the solar wind, particularly in the high-speed streams, and in planetary magnetospheres.
Collins Dictionary of Astronomy © Market House Books Ltd, 2006
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References in periodicals archive ?
Interestingly, the cold plasma waves propagate like as Alfven waves which are independent of temperature.
Molevich, "Parametrical amplification of Alfven waves in heat-releasing ionized media with magnetoacoustic instability," Astrophysics and Space Science, vol.
Whether the nonthermal width is due to Alfven waves was examined by observing coronal loops with different orientations, (31) and it was found that the nonthermal motions are nearly isotropic.
Nakamura et al., "Giant chromospheric anemone jet observed with Hinode and comparison with magnetohydrodynamic simulations: Evidence of propagating Alfven waves and magnetic reconnection," The Astrophysical Journal Letters, vol.
The gyrokinetic codes contain a more self-consistent description of the coupling of the Alfven eigenmodes to kinetic Alfven waves. The linear gyrokinetic calculations were more consistent with the experimental observations of higher damping rates in JET plasmas where continuum damping was avoided.
First, we studied the dispersion relation of parallel propagating EMIC waves, which have three modes: H-EMIC waves, [.sup.4.He]-EMIC waves, and Alfven waves. Second, we investigated the preferential heating of [.sup.3.He] and heavy ions by the EMIC waves.
The magnetic waves, called Alfven waves, are considered the most plausible explanation for the transfer of so much energy from the sun's surface to its corona.
The result, rather than being a collection of papers, is an organized text with a logical order of topics, including accretion discs, discs with magnetohydrodynamic (MHD) turbulence and their response to orbiting planets, mixing at the surface of white dwarf stars, pulsar magnetospheres, magnetic fields in galaxies, self-consistent mean field electrodynamics in two and three dimensions, magnetoconversion, Alfven waves within the earth's core, turbulence models and plane layer dynamos, planetary and stellar dynamos, convection in rotating spherical fluid shells and its dynamic states, laboratory experiments on liquid metal dynamos and liquid metal MHD turbulence and formation and stability in the solar system.
2), which may be satisfactorily interpreted in terms of an enhanced absorption of downgoing Alfven waves through the perturbed lower ionosphere.
The Alfven waves in this case tended to have great consistency in height-or amplitude, which is the common term when talking about waves-but they are random in direction.
In extremely powerful flares, CME-associated shock fronts can force overlying ions and magnetic fields to oscillate in traveling waves (magnetohydrodynamic or Alfven waves) that reach supersonic velocities and trigger similar but slower-drifting and longer-lasting radio emissions from coronal plasma waves (Type II bursts).
Instruments onboard, including those built at University of New Hampshire's Space Science Center, sampled electric and magnetic fields as well as charged particles in Earth's upper atmosphere (ionosphere) that get sloshed back and forth by a specific form of electromagnetic energy known as Alfven waves.

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